共查询到20条相似文献，搜索用时 265 毫秒
1.
We derive exact time-domain solutions for scattering of acoustic waves by a half plane by inverse Fourier transforming the frequency-domain integral solutions. The solutions consist of a direct term, a reflected term and two diffraction terms. The diffracting edge induces step function discontinuities in the direct and reflected, terms at two shadow boundries. At each boundary, the associated diffraction term reaches a maximum amplitude of half the geometrical optics term and has a signum function discontinuity so that the total field remains continuous. We evaluate solutions for practical point source configurations by numerically convolving the impulse diffraction responses with a wavelet. We solve the associated problems of convolution with a singular, truncated diffraction operator by analytically derived correction techniques. We produce a zero offset section and compare it to a Kirchhoff integral solution. Our exact diffraction hyperbola exhibits noticeable asymmetry, with higher amplitudes on the reflector side of the edge. Near the apex of the hyperbola the Kirchhoff solution approximates the exact diffraction term symmetric in amplitude about the reflection shadow boundary, but omits the other low amplitude term necessary to ensure continuity at the direct shadow boundary. 相似文献
2.
As an ideal carrier of high-resolution information, seismic diffraction can be used to clarify and locate small-scale discontinuities or inhomogeneities in the subsurface. However, a diffraction is weak and thus be suppressed by the specular reflection. Furthermore, a diffraction would be destroyed by the conventional imaging method due to the polarity reversal of diffraction. In this paper, we analyse the behaviour of diffraction and reflection. For the image point on a horizontal or oblique reflector, the zone on both sides of the stationary point has the same energy after using a cosine weight function. Based on the behaviour, we propose the adaptive phase filter to adjust the polarity of the energy on both sides, and calculate it through the illumination angle and the reflector dip angle. This method avoids the calculation of the Fresnel zones and can further suppress residual reflection that disturb the diffraction images. Synthetic and field data applications show that the desired imaging results can be obtained by the proposed method. The test results demonstrate that the method is efficient in detecting small-scale discontinuities or inhomogeneities in the subsurface and can provide high-resolution information for seismic interpretation. 相似文献
3.
Jianguo Sun 《Geophysical Prospecting》1996,44(3):351-374
Conventionally, the Fresnel zone and the geometrical spreading factor are investigated separately, because they belong to different theories of wave propagation. However, if the paraxial ray method is used for establishing the Fresnel–Kirchhoff diffraction formula for a laterally inhomogeneous multilayered medium, it can be shown that the normalized geometrical spreading factor is inversely proportional to the area of the first Fresnel zone associated with the reflection point. Therefore, if no diffracting edge cuts the first Fresnel zone, the geometrical optics approximation represents the principal part of the wavefield obtained by Fresnel–Kirchhoff diffraction theory. Otherwise, the geometrical optics approximation has to be corrected by adding edge diffractions. It is also shown that Kirchhoff-type migration and geometrical spreading factor correction both reduce the first Fresnel zone to a zone with unit area. 相似文献
4.
This paper is concerned with the problem of interpretation of anomalous seismic amplitudes, induced by the amplitude‐scattering phenomenon. This phenomenon occurs in the vicinity of a crack distribution at the interface between elastic layers. The purpose of this work is to obtain a better understanding of the physics of this distinctive phenomenon, in order to interpret correctly the amplitudes of the reflected events. By analogy with studies in optics and in acoustics, we suggest that diffraction is widely involved in the amplitude‐scattering phenomenon. Analytical evaluation of the amount of energy carried by the reflected and the diffracted waves shows that neglecting diffraction in numerical models leads to local underestimation of the amplitude of waves reflected at interfaces with gas‐filled crack distribution. 相似文献
5.
We propose a method for imaging small‐scale diffraction objects in complex environments in which Kirchhoff‐based approaches may fail. The proposed method is based on a separation between the specular reflection and diffraction components of the total wavefield in the migrated surface angle domain. Reverse‐time migration was utilized to produce the common image gathers. This approach provides stable and robust results in cases of complex velocity models. The separation is based on the fact that, in surface angle common image gathers, reflection events are focused at positions that correspond to the apparent dip angle of the reflectors, whereas diffracted events are distributed over a wide range of angles. The high‐resolution radon‐based procedure is used to efficiently separate the reflection and diffraction wavefields. In this study, we consider poststack diffraction imaging. The advantages of working in the poststack domain are its numerical efficiency and the reduced computational time. The numerical results show that the proposed method is able to image diffraction objects in complex environments. The application of the method to a real seismic dataset illustrates the capability of the approach to extract diffractions. 相似文献
6.
One of the problems encountered in a variety of near-surface investigations is detecting and mapping localized heterogeneities. The heterogeneities may be classified under two kinds of objects: (1) a point diffractor that can be considered as an approximation of a small quasi-isometric, such as small karstic cavities and caves; (2) a linear diffractor roughly approximating an elongated object, such as a tube or fault plane. The point and linear diffractors generate two types of seismic diffraction: tip and edge waves, respectively. During the last few decades, different methods were proposed by many researchers for detecting these heterogeneities utilizing seismic waves diffracted by them. An alternative method for detecting point diffractors using a time-reversal principle combined with focusing analysis is proposed in this study: we present an extension of the time-reversal method for linear diffractors. It consists of a coherent summation of seismic energy along edge-diffraction traveltimes. Real data examples show the feasibility and efficiency of the proposed method. 相似文献
7.
Diffraction of seismic waves in an elastic, cracked halfplane using a boundary integral formulation 总被引：1，自引：0，他引：1
A. Rodríguez-Castellanos F. Luzn F.J. Snchez-Sesma 《Soil Dynamics and Earthquake Engineering》2005,25(11):827-837
The presence of subsurface cracks in a halfspace excited by elastic waves may give rise to scattered body and surface waves. For many engineering applications, such as non-destructive testing or oil exploration, the scattered field may yield valuable information to detect cracks and other scatterers. We use the Indirect Boundary Element Method (IBEM) to study the diffraction of P, SV waves with various incidence angles and Rayleigh surface waves. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. Our approach is usually called indirect BEM as the sources' strengths should be obtained as an intermediate step. This indirect formulation can give to the analyst a deep physical insight on the generated diffracted waves because it is closer to the physical reality and can be regarded as a realization of Huygens' Principle. In any event, mathematically it is fully equivalent to the classical Somigliana's representation theorem. In order to gauge accuracy we test our method by comparing with previous results in the literature. Various crack configurations, including multiple cracks, are investigated. Results in frequency and time domains are displayed. Under certain conditions the amplitude spectra of those waves clearly show conspicuous resonance peaks. 相似文献
8.
Diffractions play a vital role in seismic processing as they can be utilized for high‐resolution imaging applications and analysis of subsurface medium properties like velocity. They are particularly valuable for anisotropic media as they inherently possess a wide range of dips necessary to resolve the angular dependence of velocity. However, until recently, the focus of diffraction imaging or inversion algorithms have been only on the isotropic approximation of the subsurface. Using diffracted waves, we develop a framework to invert for the effective η model. This effective model is obtained through scanning over possible effective η values and selecting the one that best fits the observed moveout curve for each diffractor location. The obtained effective η model is then converted to an interval η model using a Dix‐type inversion formula. The inversion methodology holds the potential to reconstruct the true η model with sufficiently high accuracy and resolution properties. However, it relies on an accurate estimation of diffractor locations, which in turn requires good knowledge of the background velocity model. We test the effectiveness and applicability of our method on the vertical transverse isotropic Marmousi model. The inversion results yield a reasonable match even for the complex Marmousi model. 相似文献
9.
It is well‐known that experimental or numerical backpropagation of waves generated by a point‐source/‐scatterer will refocus on a diffraction‐limited spot with a size not smaller than half the wavelength. More recently, however, super‐resolution techniques have been introduced that apparently can overcome this fundamental physical limit. This paper provides a framework of understanding and analysing both diffraction‐limited imaging as well as super resolution. The resolution analysis presented in the first part of this paper unifies the different ideas of backpropagation and resolution known from the literature and provides an improved platform to understand the cause of diffraction‐limited imaging. It is demonstrated that the monochromatic resolution function consists of both causal and non‐causal parts even for ideal acquisition geometries. This is caused by the inherent properties of backpropagation not including the evanescent field contributions. As a consequence, only a diffraction‐limited focus can be obtained unless there are ideal acquisition surfaces and an infinite source‐frequency band. In the literature various attempts have been made to obtain images resolved beyond the classical diffraction limit, e.g., super resolution. The main direction of research has been to exploit the evanescent field components. However, this approach is not practical in case of seismic imaging in general since the evanescent waves are so weak – because of attenuation, they are masked by the noise. Alternatively, improvement of the image resolution of point like targets beyond the diffraction limit can apparently be obtained employing concepts adapted from conventional statistical multiple signal classification (MUSIC). The basis of this approach is the decomposition of the measurements into two orthogonal domains: signal and noise (nil) spaces. On comparison with Kirchhoff prestack migration this technique is showed to give superior results for monochromatic data. However, in case of random noise the super‐ resolution power breaks down when employing monochromatic data and a limited acquisition aperture. For such cases it also seems that when the source‐receiver lay out is less correlated, the use of a frequency band may restore the super‐resolution capability of the method. 相似文献
10.
The role played by the diffraction field on the problem of seismic site effects is studied. For that purpose we solve and analyze simple scattering problems under P and SV in-plane wave assumptions, using two well known direct boundary-element-based numerical methods. After establishing the difference between scattered and diffracted motions, and introducing the concept of artificious and physically based incoming fields, we obtain the amplitude of the Fourier spectra for the diffracted part of the response: this is achieved after establishing the connection between the spatial distribution of the transfer function over the studied simple topographies and the diffracted field. From the numerical simulations it is observed that this diffracted part of the response is responsible for the amplification of the surface ground motions due to the geometric effect. Furthermore, it is also found that the diffraction field sets in a fingerprint of the topographic effect in the total ground motions. These conclusions are further supported by observations in the time-domain in terms of snapshots of the propagation patterns over the complete computational model. In this sense the geometric singularities are clearly identified as sources of diffraction and for the considered range of dimensionless frequencies it is evident that larger amplifications are obtained for the geometries containing a larger number of diffraction sources thus resulting in a stronger topographic effect. The need for closed-form solutions of canonical problems to construct a robust analysis method based on the diffraction field is identified. 相似文献
11.
地震绕射波是地下非连续性地质体的地震响应,绕射波成像对地下断层、尖灭和小尺度绕射体的识别具有重要的意义.在倾角域共成像点道集中,反射波同相轴表现为一条下凸曲线,能量主要集中在菲涅耳带内,绕射波能量则比较发散.由于倾角域菲涅耳带随偏移距变化而存在差异,因此本文提出一种在倾角-偏移距域道集中精确估计菲涅耳带的方法,在各偏移距的倾角域共成像点道集中实现菲涅耳带的精确切除,从而压制反射波.在倾角-偏移距域道集中还可以分别实现绕射波增强,绕射波同相轴相位校正,因此能量弱的绕射波可以清晰地成像.在倾角域共成像点道集中,反射波同相轴的最低点对应于菲涅耳带估计所用的倾角,因此本文提出一种在倾角域共成像点道集中直接自动拾取倾角场的方法.理论与实际资料试算验证了本文绕射波成像方法的有效性. 相似文献
12.
Konstantin Tertyshnikov Roman Pevzner Andrej Bóna Faisal Alonaizi Boris Gurevich 《Geophysical Prospecting》2015,63(3):525-533
Hard rock seismic exploration normally has to deal with rather complex geological environments. These types of environments are usually characterized by a large number of local heterogeneity (e.g., faults, fracture zones, and steeply dipping interfaces). The seismic data from such environments often have a poor signal‐to‐noise ratio because of the complexity of hard rock geology. To be able to obtain reliable images of subsurface structures in such geological conditions, processing algorithms that are capable of handling seismic data with a low signal‐to‐noise ratio are required for a reflection seismic exploration. In this paper, we describe a modification of the 3D Kirchhoff post‐stack migration algorithm that utilizes coherency attributes obtained by the diffraction imaging algorithm in 3D to steer the main Kirchhoff summation. The application to a 3D synthetic model shows the stability of the presented steered migration to the presence of high level of the random noise. A test on the 3D seismic volume, acquired on a mine site located in Western Australia, reveals the capability of the approach to image steep and sharp objects such as fracture and fault zones and lateral heterogeneity. 相似文献
13.
Finite-offset seismic reflection modeling of acoustic waves, propagating in a two-dimensional depth section of arbitrary complexity, is discussed. The procedure developed employs the principles of simplified (far-field) diffractor theory and ray tracing. Each reflector is represented by a set of discrete secondary sources or diffractors and the wavefield associated with each diffractor is calculated directly in the time domain by ray tracing. Reflections and diffractions are subsequently built up by the numerical superposition of these wavefields. This superposition is nondispersive for all frequencies for which the Fresnel zones are large compared with the diffractor separation. All primary travel paths connecting the shot to diffractor and diffractor to geophone are accounted for together with phase changes induced by focal events. The method allows the modeling of arbitrary trace gathers for energy originating from selected reflectors. The nonsequential nature of the algorithm makes it suited to machines capable of carrying out many similar operations in parallel or concurrently. Diffractor theory also provides physical insight into wave scattering and focusing. In particular, the half-differential waveform associated with a line diffractor leads to an explanation of the 90° phase lead induced by a cylindrical focus and, similarly, the full differential waveform of a point diffractor can be used to explain the 180° phase shift induced by a point focus. 相似文献
14.
Sea‐bed diffractions are frequently observed for several of the fields in the Norwegian Sea and the Barents Sea. This is a challenge in time lapse seismic analysis, since diffracted multiples are difficult to remove by processing and therefore is a major source of poor time lapse data quality. In this work we test if the diffractions can be used for enhanced 4D interpretation. By analysing the time‐shift of the sea‐bed diffraction hyperbola between the base and monitor it is tested if changes in water velocity and tides can be estimated. Two models using time lapse diffraction analysis are tested: the first one simply adds time‐shifts for the two branches of the diffraction hyperbola and this average time‐shift is then used to estimate the water velocity change. The other method uses an inversion method based on the diffraction equation for a point diffractor to estimate the velocity change. In‐line common‐midpoint shifts are estimated by subtracting the time‐shifts of both hyperbola branches followed by direct inversion. The diffraction based time‐shifts are compared to time‐shifts estimated by standard cross‐correlation of the sea‐bed reflection. The averaging method gives slightly higher uncertainties, while the inversion using an exact traveltime equation gives similar uncertainties compared to the sea‐bed reflection method. 相似文献
15.
Margarita Luneva 《Pure and Applied Geophysics》1996,148(1-2):113-136
Numerical examples of high-frequency synthetic seismograms of body waves in a 2-D layered medium with complex interfaces (faults, wedges, curvilinear, corrugated) are presented. The wave field modeling algorithm combines the possibilities of the ray method and the edge wave superposition method. This approach preserves all advantages of the ray method and eliminates restrictions related to diffraction by boundary edges and to caustic effects in singular regions. The method does not require two-point ray tracing (source-to-receiver), and the position of the source, as well as the type of source, and the position of receivers can be chosen arbitrarily. The memory and the time required for synthetic seismogram computation are similar to ray synthetic seismograms. The computation of the volume of the medium (the Fresnel volume or Fresnel zones), which gives the essential contribution to the wave field, is included in the modeling program package. In the case of complicated irregular interface (or a layered medium with a regular ray field at the last interface), the method displays a high accuracy of wave field computation. Otherwise, the method can be considered a modification of the ray method with regularization by the superposition of edge waves. 相似文献
16.
Common‐shot Fresnel beam migration based on wave‐field approximation in effective vicinity under complex topographic conditions 
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下载免费PDF全文 Gaussian beam migration is a versatile imaging method for geologically complex land areas, which overcomes the limitation of Kirchhoff migration in imaging multiple arrivals and has no steep‐dip limits of one‐way wave‐equation migration. However, its imaging accuracy depends on the geometry of Gaussian beam that is determined by the initial parameter of dynamic ray tracing. As a result, its applications in exploration areas with strong variations in topography and near‐surface velocity are limited. Combined with the concept of Fresnel zone and the theory of wave‐field approximation in effective vicinity, we present a more robust common‐shot Fresnel beam imaging method for complex topographic land areas in this paper. Compared with the conventional Gaussian beam migration for irregular topography, our method improves the beam geometry by limiting its effective half‐width with Fresnel zone radius. Moreover, through a quadratic travel‐time correction and an amplitude correction that is based on the wave‐field approximation in effective vicinity, it gives an accurate method for plane‐wave decomposition at complex topography, which produces good imaging results in both shallow and deep zones. Trials of two typical models and its application in field data demonstrated the validity and robustness of our method. 相似文献
17.
Parsimonious post‐stack migration is extended to three dimensions. By tracing single rays back along each incident wave direction (as determined by a local slant stack at the receivers), the ray tracing can be embedded in the migration. This approach significantly reduces the computer time and disk space needed because it is not necessary to build and save image time maps; 3D migration can be performed on a workstation or personal computer rather than using a supercomputer or cluster. The location of a reflector in the output image is defined by tracing a zero‐offset ray to the one‐way traveltime (the image condition); the orientation of the reflector is defined as a surface perpendicular to the raypath. The migration impulse response operator is confined to the first Fresnel zone around the estimated reflection point, which is much smaller than the large isochronic surface in traditional Kirchhoff depth migration. Additional efficiency is obtained by applying an amplitude threshold to reduce the amount of data to be migrated. Tests on synthetic data show that the proposed implementation of parsimonious 3D post‐stack Kirchhoff depth migration is at least two orders of magnitude faster than traditional Kirchhoff migration, at the expense of slightly degraded migration image coherence. The proposed migration is expected to be a useful complement to conventional time migrations for fast initial imaging of subsurface structures and for real‐time imaging of near‐offset sections during data acquisition for quality control. 相似文献
18.
Results of studies carried out with the help of a three-dimensional seismic model on waves diffracted from edges of varying radius of curvature R and depth h with respect to wave length λ are described. The amplitude decay, travel time, and apparent velocity of the wave diffracted from a sub-surface edge of semi-infinite length are found to depend on the parameters R, h, and distance from the edge on the surface provided the ratio of the parameters to λ are less than some limiting values. The nature of the amplitude decay is independent of R when the depth exceeds 2λ, and independent of h when R exceeds 1.5λ. When these are below the limiting values (h= 2λ and R= 1.5λ), the nature of the decay depends appreciably on R and h. The apparent decay in amplitude on the surface due to geometrical spreading by the diffracting edge is less than that of a cylindrical secondary wave source and decreases with increase in depth of the edge. The nature of the travel time curves of the diffracted waves near the edge depend on R/λ when the depth is within about one λ. Apparent velocity of the wave depends largely on R/λ in the zone of diffraction up to a distance of about one λ from the edge on the surface. Beyond this distance the velocity is almost the same irrespective of R/λ and depend only on h/λ. The width of the zone of diffraction caused by an edge of finite length comparable to λ is more and more narrow as the ratio of the distance of the edge on the surface to its depth increases. 相似文献
19.
True-amplitude (TA) migration, which is a Kirchhoff-type modified weighted diffraction stack, recovers (possibly) complex angle-dependent reflection coefficients which are important for amplitude-versus-offset (AVO) inversion. The method can be implemented using existing prestack or post-stack Kirchhoff migration and fast Green's function computation programs. Here, it is applied to synthetic single-shot and constant-offset seismic data that include post-critical reflections (complex reflection coefficients) and caustics. Comparisons of the amplitudes of the TA migration image with theoretical reflection coefficients show that the (possibly complex) angle-dependent reflection coefficients are correctly estimated. 相似文献
20.
针对接收函数正演与偏移, 本文采用波动方程有限差分算法. 借鉴成熟的勘探地震学方法, 引入等效速度概念, 建立接收函数转换波与地震勘探反射波的等效走时方程, 实现了基于波动方程有限差分算法的接收函数正演与偏移. 数值计算表明, 波动方程有限差分叠后偏移方法可以对点绕射和穹隆构造模型实现高精度成像. 本文利用数值计算讨论了波动方程有限差分叠后偏移与Kirchhoff叠后偏移对于接收函数偏移的适用性, 还对偏移过程中速度模型的误差进行了分析. 相似文献